In this paper, a novel axial flux magnetically geared machine (AFMG) is presented. The proposed AFMG machine consists of stator segments equipped with concentrated windings and two permanent magnet (PM) rotors with different pole-pair numbers. The proposed AFMG offers the merit of simple mechanical structure and is suitable for applications with limited axial space. To maximize the torque, both 2D and 3D optimizations of the machine are conducted and compared. By utilizing ANSYS Maxwell 2D finite element (FE) analysis, the global optimization based on a genetic algorithm is executed under fixed copper loss. Then, with the aid of JMAG 3D FE analysis, the optimization of individual geometry parameters is investigated. As the proposed machine has a high - speed rotor of 5 pole pairs, a low-speed rotor of 7 pole pairs, and 12 stator/modulator pieces with concentrated windings, a good agreement of optimized machine dimensions obtained from two optimization methods is achieved. Moreover, both no-load and on-load performance of the machine are analysed.